Question

Two point charges , q_{1} = 33.8nC and q_{2} = 12.6nC are located on the x-at x = 0 and x=1.00 m. respectively . Where on the x-axis the electric field equal to zero?

Answer 1

Given:

$q_1=33.8*10^{-9}\:\rm C$

$q_2=12.6*10^{-9}\:\rm C$

$d=1.00\:\rm m$

The electric field at the point A is zero. Hence

$$E_1=E_2$$

$$k\frac{q_1}{x^2}=k\frac{q_2}{(d-x)^2}$$

$$(d-x)\sqrt{q_1}=x\sqrt{q_2}$$

$$x=\frac{d\sqrt{q_1}}{\sqrt{q_1}+\sqrt{q_2}}=d*\frac{1}{1+\sqrt{q_2/q_1}}$$

$$x=1.00*\frac{1}{1+\sqrt{12.6/33.8}}=0.62\:\rm m$$